By Jeff Hwang
Like other traditional casino table games, baccarat is a single-bet, no-decision game where each independent bet represents the entirety of the game; at a baccarat table with a $5 minimum wager, a player can bet the $5 minimum and get to showdown on every hand without having to place another wager. In contrast, as we’ve noted, a distinguishing feature of poker-based table games is that they are generally multi-stage games requiring multiple wagers to get to showdown. Moreover, the average amount wagered on a per-hand basis varies greatly among the different poker variants.
This average amount wagered per hand on a unit basis is the average bet per hand.
In Three Card Poker, for example, the player starts with an initial Ante wager, and is correct to make the one-unit Play bet whenever he is dealt Q-6-4 or better, which happens on 67.4% of deals. Thus, on average, the player wagers:
1 + (.674)(1) = 1.67 units
In Four Card Poker, the player makes an Ante wager, and then can bet 1x-3x the ante or fold after receiving five down cards (the player’s best four-card poker hand plays). Played optimally, the player will make the minimum one-unit bet on 22.1% of hands, and bet the 3x maximum on 30.7% of hands, while never betting 2x. Thus the average bet per hand under optimal play is:
1 + (.221)(1) + (.307)(3) = 2.14 units
In Crazy 4 Poker, the player starts with two initial wagers – an Ante wager and a Super Bonus bet – and can bet 1x-3x the ante or fold on his five down cards. The player can only bet 3x on a pair of aces or better, which occurs on 18.6% of hands, while betting the minimum one unit on 57.9% of hands (K-Q-8-4+). This results in an average bet per hand of:
2 + (.579)(1) + (.186)(3) = 3.14 units
Meanwhile, in Ultimate Texas Hold’em, the player starts with two initial wagers – an Ante wager and a Blind wager – and has three opportunities to bet once: The player can either bet 3x-4x the ante before the flop, or 2x on the flop, or 1x on the river. Played optimally, the player makes the 4x maximum bet on 37.7% of hands, the 2x flop wager on 21.3% of hands, and the minimum 1x bet on the river on 21.8% of hands, resulting an average bet per hand of:
2 + (.377)(4) + (.213)(2) + (.218)(1) = 4.15 units
The average bet per hand for some of the more prominent games currently on the market are listed in the table below.
Note: Michael Shackleford a.k.a. Wizard of Odds refers to this number as “Average Bet Size,” but I have another use for that term (referring more specifically to the size of the play or raise bet), and prefer to refer to the average bet per hand as what it is.
Like other traditional casino table games, baccarat is a single-bet, no-decision game where each independent bet represents the entirety of the game; at a baccarat table with a $5 minimum wager, a player can bet the $5 minimum and get to showdown on every hand without having to place another wager. In contrast, as we’ve noted, a distinguishing feature of poker-based table games is that they are generally multi-stage games requiring multiple wagers to get to showdown. Moreover, the average amount wagered on a per-hand basis varies greatly among the different poker variants.
This average amount wagered per hand on a unit basis is the average bet per hand.
In Three Card Poker, for example, the player starts with an initial Ante wager, and is correct to make the one-unit Play bet whenever he is dealt Q-6-4 or better, which happens on 67.4% of deals. Thus, on average, the player wagers:
1 + (.674)(1) = 1.67 units
In Four Card Poker, the player makes an Ante wager, and then can bet 1x-3x the ante or fold after receiving five down cards (the player’s best four-card poker hand plays). Played optimally, the player will make the minimum one-unit bet on 22.1% of hands, and bet the 3x maximum on 30.7% of hands, while never betting 2x. Thus the average bet per hand under optimal play is:
1 + (.221)(1) + (.307)(3) = 2.14 units
In Crazy 4 Poker, the player starts with two initial wagers – an Ante wager and a Super Bonus bet – and can bet 1x-3x the ante or fold on his five down cards. The player can only bet 3x on a pair of aces or better, which occurs on 18.6% of hands, while betting the minimum one unit on 57.9% of hands (K-Q-8-4+). This results in an average bet per hand of:
2 + (.579)(1) + (.186)(3) = 3.14 units
Meanwhile, in Ultimate Texas Hold’em, the player starts with two initial wagers – an Ante wager and a Blind wager – and has three opportunities to bet once: The player can either bet 3x-4x the ante before the flop, or 2x on the flop, or 1x on the river. Played optimally, the player makes the 4x maximum bet on 37.7% of hands, the 2x flop wager on 21.3% of hands, and the minimum 1x bet on the river on 21.8% of hands, resulting an average bet per hand of:
2 + (.377)(4) + (.213)(2) + (.218)(1) = 4.15 units
The average bet per hand for some of the more prominent games currently on the market are listed in the table below.
Note: Michael Shackleford a.k.a. Wizard of Odds refers to this number as “Average Bet Size,” but I have another use for that term (referring more specifically to the size of the play or raise bet), and prefer to refer to the average bet per hand as what it is.
Average Bet Per Hand
| Game Ultimate Texas Hold’em Mississippi Stud** Crazy 4 Poker Four Card Poker Caribbean Stud High Card Flush Three Card Poker | Forced Bets 2 1 2 1 1 1 1 | Min-Bet Frequency 21.8%* 63.0% 57.9% 22.1% 52.2% 64.9% 67.4% | Max-Bet Frequency 37.7% 5.9% 18.6% 30.7% -- 3.1% -- | Total Bet Frequency 80.8% 68.9% 76.5% 52.8% 52.2% 67.9% 67.4% | Avg. Bet Per Hand 4.15 Units 3.59 Units 3.14 Units 2.14 Units 2.04 Units 1.71 Units 1.67 Units |
Source: wizardofodds.com
*The player also bets 2x on the flop on 21.3% of hands
**Reflects 3rd Street betting only; the player makes a maximum 3x bet on at least one betting round on 21.2% of hands, while betting the maximum on all three betting rounds on 4.1% of hands
*The player also bets 2x on the flop on 21.3% of hands
**Reflects 3rd Street betting only; the player makes a maximum 3x bet on at least one betting round on 21.2% of hands, while betting the maximum on all three betting rounds on 4.1% of hands
So what does this mean? Is a higher average bet per hand a good thing or a bad thing?
The answer is that a higher average bet per hand is neither fundamentally a good nor bad thing, but it does reflect to an extent how aggressive a game is. For instance, the top four games on this list all feature scalable betting, while the top game – Ultimate Texas Hold’em – has a max-bet frequency of 37.7%, and Four Card Poker also features a relatively high max-bet frequency of 30.7%.
Another major implication is that games with higher average bets per hand are fundamentally higher stakes games, given equal table minimums. A baccarat table with a $5 minimum wager is a true $5 minimum game, but a $5-min Three Card Poker table with an average bet of 1.67 units per hand is effectively an $8.35-minimum game. At the same time, an Ultimate Texas Hold’em table with a $5 stated table minimum has two forced bets and an average bet of 4.15 units per hand, for a true effective table minimum – that is, the minimum average wager per hand under optimal play given the stated table minimum – of $20.75 per hand.
Consequently, a $5-minium Ultimate Texas Hold’em table is closer in stakes to a $25-minimum blackjack table than a $5-minimum one, and closer in stakes to a Three Card Poker table with a $15 minimum bet (effective table minimum of $25.05) than one with a $5 minimum bet.
The answer is that a higher average bet per hand is neither fundamentally a good nor bad thing, but it does reflect to an extent how aggressive a game is. For instance, the top four games on this list all feature scalable betting, while the top game – Ultimate Texas Hold’em – has a max-bet frequency of 37.7%, and Four Card Poker also features a relatively high max-bet frequency of 30.7%.
Another major implication is that games with higher average bets per hand are fundamentally higher stakes games, given equal table minimums. A baccarat table with a $5 minimum wager is a true $5 minimum game, but a $5-min Three Card Poker table with an average bet of 1.67 units per hand is effectively an $8.35-minimum game. At the same time, an Ultimate Texas Hold’em table with a $5 stated table minimum has two forced bets and an average bet of 4.15 units per hand, for a true effective table minimum – that is, the minimum average wager per hand under optimal play given the stated table minimum – of $20.75 per hand.
Consequently, a $5-minium Ultimate Texas Hold’em table is closer in stakes to a $25-minimum blackjack table than a $5-minimum one, and closer in stakes to a Three Card Poker table with a $15 minimum bet (effective table minimum of $25.05) than one with a $5 minimum bet.
Effective Table Minimum
| Game Ultimate Texas Hold’em Mississippi Stud Crazy 4 Poker Four Card Poker Caribbean Stud High Card Flush Three Card Poker | Stated Table Minimum $5 $5 $5 $5 $5 $5 $5 | Forced Bets 2 1 2 1 1 1 1 | Avg. Bet Per Hand 4.15 Units 3.59 Units 3.14 Units 2.14 Units 2.04 Units 1.71 Units 1.67 Units | Effective Table Minimum $20.75 $17.95 $15.70 $10.70 $10.22 $8.56 $8.35 |
And along with house advantage, the average bet per hand is also a key variable in Shackleford’s element of risk, which we’ll discuss next.
Next: House Advantage and Element of Risk
Jeff Hwang is President and CEO of High Variance Games LLC. Jeff is also the best-selling author of Pot-Limit Omaha Poker: The Big Play Strategy and the three-volume Advanced Pot-Limit Omaha series.
Next: House Advantage and Element of Risk
Jeff Hwang is President and CEO of High Variance Games LLC. Jeff is also the best-selling author of Pot-Limit Omaha Poker: The Big Play Strategy and the three-volume Advanced Pot-Limit Omaha series.
